A121663 a(0) = 1; if n = 2^k, a(n) = k+2, otherwise a(n)=(A000523(n)+2)*a(A053645(n)).

1, 2, 3, 6, 4, 8, 12, 24, 5, 10, 15, 30, 20, 40, 60, 120, 6, 12, 18, 36, 24, 48, 72, 144, 30, 60, 90, 180, 120, 240, 360, 720, 7, 14, 21, 42, 28, 56, 84, 168, 35, 70, 105, 210, 140, 280, 420, 840, 42, 84, 126, 252, 168, 336, 504, 1008, 210, 420, 630, 1260, 840, 1680

Offset: 0

Author

Antti Karttunen, Aug 25 2006

Keywords

• nonn

Comments

Each n occurs A045778(n) times in the sequence.

Links

• Ivan Neretin, Table of n, a(n) for n = 0..8192

Crossrefs

Bisection of A096111.

Programs

Mathematica

f[0] := 1; f[n_] := If[(b = n - 2^(k = Floor[Log2[n]])) == 0, k + 2, (k + 2)*f[b]]; Table[f[n], {n, 0, 61}] (* Ivan Neretin, May 09 2015 *)

Scheme

(define (A121663 n) (cond ((zero? n) 1) ((pow2? n) (+ 2 (A000523 n))) (else (* (+ 2 (A000523 n)) (A121663 (A053645 n))))))
(define (pow2? n) (and (> n 0) (zero? (A004198bi n (- n 1)))))

Formula

G.f.: Product_{k>=0} (1 + (k + 2) * x^(2^k)). - Ilya Gutkovskiy, Aug 19 2019